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Towards Higher-Order Zeroing Neural Networks for Calculating Quaternion Matrix Inverse with Application to Robotic Motion Tracking

Author

Listed:
  • Rabeh Abbassi

    (Department of Electrical Engineering, College of Engineering, University of Hail, Hail 81451, Saudi Arabia)

  • Houssem Jerbi

    (Department of Industrial Engineering, College of Engineering, University of Hail, Hail 81451, Saudi Arabia)

  • Mourad Kchaou

    (Department of Electrical Engineering, College of Engineering, University of Hail, Hail 81451, Saudi Arabia)

  • Theodore E. Simos

    (Center for Applied Mathematics and Bioinformatics, Gulf University for Science and Technology, West Mishref 32093, Kuwait
    Laboratory of Inter-Disciplinary Problems of Energy Production, Ulyanovsk State Technical University, 32 Severny Venetz Street, 432027 Ulyanovsk, Russia
    Department of Medical Research, China Medical University Hospital, China Medical University, Taichung City 40402, Taiwan
    Data Recovery Key Laboratory of Sichun Province, Neijing Normal University, Neijiang 641100, China)

  • Spyridon D. Mourtas

    (Department of Economics, Mathematics-Informatics and Statistics-Econometrics, National and Kapodistrian University of Athens, Sofokleous 1 Street, 10559 Athens, Greece
    Laboratory “Hybrid Methods of Modelling and Optimization in Complex Systems”, Siberian Federal University, Prosp. Svobodny 79, 660041 Krasnoyarsk, Russia)

  • Vasilios N. Katsikis

    (Department of Economics, Mathematics-Informatics and Statistics-Econometrics, National and Kapodistrian University of Athens, Sofokleous 1 Street, 10559 Athens, Greece)

Abstract

The efficient solution of the time-varying quaternion matrix inverse (TVQ-INV) is a challenging but crucial topic due to the significance of quaternions in many disciplines, including physics, engineering, and computer science. The main goal of this research is to employ the higher-order zeroing neural network (HZNN) strategy to address the TVQ-INV problem. HZNN is a family of zeroing neural network models that correlates to the hyperpower family of iterative methods with adjustable convergence order. Particularly, three novel HZNN models are created in order to solve the TVQ-INV both directly in the quaternion domain and indirectly in the complex and real domains. The noise-handling version of these models is also presented, and the performance of these models under various types of noises is theoretically and numerically tested. The effectiveness and practicality of these models are further supported by their use in robotic motion tracking. According to the principal results, each of these six models can solve the TVQ-INV effectively, and the HZNN strategy offers a faster convergence rate than the conventional zeroing neural network strategy.

Suggested Citation

  • Rabeh Abbassi & Houssem Jerbi & Mourad Kchaou & Theodore E. Simos & Spyridon D. Mourtas & Vasilios N. Katsikis, 2023. "Towards Higher-Order Zeroing Neural Networks for Calculating Quaternion Matrix Inverse with Application to Robotic Motion Tracking," Mathematics, MDPI, vol. 11(12), pages 1-21, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:12:p:2756-:d:1173657
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    References listed on IDEAS

    as
    1. Zi-Hua Weng, 2014. "Field Equations in the Complex Quaternion Spaces," Advances in Mathematical Physics, Hindawi, vol. 2014, pages 1-6, August.
    2. Vladislav N. Kovalnogov & Ruslan V. Fedorov & Dmitry A. Generalov & Andrey V. Chukalin & Vasilios N. Katsikis & Spyridon D. Mourtas & Theodore E. Simos, 2022. "Portfolio Insurance through Error-Correction Neural Networks," Mathematics, MDPI, vol. 10(18), pages 1-14, September.
    3. Spyridon D. Mourtas & Chrysostomos Kasimis, 2022. "Exploiting Mean-Variance Portfolio Optimization Problems through Zeroing Neural Networks," Mathematics, MDPI, vol. 10(17), pages 1-20, August.
    4. Wendong Jiang & Chia-Liang Lin & Vasilios N. Katsikis & Spyridon D. Mourtas & Predrag S. Stanimirović & Theodore E. Simos, 2022. "Zeroing Neural Network Approaches Based on Direct and Indirect Methods for Solving the Yang–Baxter-like Matrix Equation," Mathematics, MDPI, vol. 10(11), pages 1-13, June.
    5. Spyridon D. Mourtas, 2022. "A weights direct determination neuronet for time‐series with applications in the industrial indices of the Federal Reserve Bank of St. Louis," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 41(7), pages 1512-1524, November.
    6. Mariya Kornilova & Vladislav Kovalnogov & Ruslan Fedorov & Mansur Zamaleev & Vasilios N. Katsikis & Spyridon D. Mourtas & Theodore E. Simos, 2022. "Zeroing Neural Network for Pseudoinversion of an Arbitrary Time-Varying Matrix Based on Singular Value Decomposition," Mathematics, MDPI, vol. 10(8), pages 1-12, April.
    7. Houssem Jerbi & Izzat Al-Darraji & Georgios Tsaramirsis & Lotfi Ladhar & Mohamed Omri, 2023. "Hamilton–Jacobi Inequality Adaptive Robust Learning Tracking Controller of Wearable Robotic Knee System," Mathematics, MDPI, vol. 11(6), pages 1-32, March.
    8. Jun Yang & Jing Na & Guanbin Gao & Chao Zhang, 2018. "Adaptive Neural Tracking Control of Robotic Manipulators with Guaranteed NN Weight Convergence," Complexity, Hindawi, vol. 2018, pages 1-11, October.
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    Cited by:

    1. Houssem Jerbi & Obaid Alshammari & Sondess Ben Aoun & Mourad Kchaou & Theodore E. Simos & Spyridon D. Mourtas & Vasilios N. Katsikis, 2023. "Hermitian Solutions of the Quaternion Algebraic Riccati Equations through Zeroing Neural Networks with Application to Quadrotor Control," Mathematics, MDPI, vol. 12(1), pages 1-19, December.

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